Deterministic chaos is not the same as randomness.

Deterministic chaos is sensitive dependence on initial conditions. (Butterfly effect)

Deterministic chaos provides short-term predictability but long-term uncertainty.

• Chaos - Wikipedia entry
• Lorenz system

Nonlinearlity is necessary for deterministic chaos, but is not sufficient.

Phase space, attractors

E.g. mass on a spring: undamped, damped, damped and driven.

Chaos, strange attractors, period doubling, period 3 implies chaos

Chaos in mathematics: nonlinear differential equations, logisitic map
Chaos in physics: dripping water, flapping flag.